Method of estimating an intersection between at least two continuous signal representations

ABSTRACT

The invention relates to a method of estimating an intersection between at least two continuous signal representations (SR 1 , SR 2 ) in a pulse width modulator, at least one of said continuous signal representations (SR 1 , SR 2 ) being non-linear, said method comprising the step of providing an intersection estimate (CPE) between said at least two continuous signal representations on the basis of at least one iteration comprising at least one iterative call of a function describing said continuous signal representations (SR 1 , SR 2 ) being non-linear and whereby said estimating of intersections are performed in a pulse width modulation modulator. According to an embodiment of the invention, a simple iterative call of the established continuous signal representation, e.g. an interpolation polynomial, will provide the desired intersection. It should be noted that the established estimate might be provided without any complicated root solving and avoiding division and even square root.

FIELD OF THE INVENTION

The present invention relates to a method of establishing anintersection estimate between two functions.

BACKGROUND OF THE INVENTION

Pulse width modulation, PWM, is used widely within the field of forinstance audio amplifiers. Generally, the available pulse widthmodulation techniques may be categorized into typically three differenttypes of pulse width modulation, natural pulse width modulation, NPWM,uniform pulse width modulation, UPWM or linearized pulse widthmodulation, hereinafter LPWM.

Generally, all pulse width modulation implies the technique oftransforming or converting an input signal into an output square wavesignal having a certain pulse width, at least partly defined by theinput signal by comparison of the input signal to a reference signal.

A short review of the general understanding of the above-mentionedgroups of pulse width modulation techniques will be given below.

Natural pulse width modulation, NPWM, typically implies the comparisonof a continuous time signal, typically an analogue waveform signal, to areference signal, typically a sawtooth signal. The output signals willthen switch between typically two output levels when the input signaland the reference signal intersect.

The natural pulse width modulation technique, NPWM, is generallyregarded as distortion free within the audio band.

Uniform pulse width modulation, UPWM, typically implies the comparisonof a discrete time signal, typically a digital wave form signal such asa PCM signal, to a reference signal, typically a sawtooth signal. Theoutput signals will then switch between typically two output levels whenthe input signal and the reference signal intersect. A well-knownproblem related to uniform pulse width modulation, UPWM, is that theinput signal, due to its discrete nature, may basically not necessarilybe represented at the time of intersection. This problem may be dealtwith in different ways, e.g. simply by accepting the error, and simplyquantizing the intersection time according to a quantizing algorithm.

In order to counteract the inherent distortion several PWM linearizationtechniques has been disclosed within the art.

Linearized pulse width modulation, LPWM, typically deals with emulationof the theoretical value of the input signal, if a sample of the inputsignal was actually present at the time of intersection between thereference signal and the input signal.

Such methods are often referred to as linearized pulse width modulation,LPWM. Prior art demonstrates linear interpolation between two adjacentinput samples to achieve the output pulse width. In other words, thelinearization algorithms typically operate on more than one sample ofthe input signal to determine the linearized output pulse width.

Thus several linearization techniques apply to first order interpolationof the input signal between the discrete samples in order to estimatethe true cross point between the input signal and the reference signal.

Other techniques implying 2nd order interpolation has been applied forthe purpose of coming closer to the “true” cross point, therebyminimizing the resultant distortion.

A problem of many of the relatively new and improved LPWM-techniques isthat the resulting improvement is relatively costly with respect tocomputing requirements. Thus, several linearized pulse width modulationtechniques require division.

Typically, prior art LPWM-techniques either do not include an algorithmto determine the pulse width, or they disadvantageously require adivision operation to compute the pulse width. Division operations arerelatively computationally inefficient in digital signal processing andrequire many more computation steps than for example addition ormultiplication operations. Additional silicon area is therefore requiredto implement techniques involving division. Generally knownimplementations do not provide computationally efficient methods toreduce harmonic distortion in pulse width modulated systems.

It is the object of the invention to provide an improved PWM-modulationtechnique featuring low harmonic distortion and computationallyefficiency.

SUMMARY OF THE INVENTION

The invention relates to a method of estimating an intersection betweenat least two continuous signal representations (SR1, SR2) in a pulsewidth modulator, at least one of said continuous signal representations(SR1, SR2) being non-linear,

said method comprising the step of providing an intersection estimate(CPE) between said at least two continuous signal representations on thebasis of at least one iteration comprising at least one iterative callof a function describing said continuous signal representations (SR1,SR2) being non-linear and whereby said estimating of intersections areperformed in a pulse width modulator.

In a preferred embodiment of the invention a pulse width modulator is apulse width amplifier.

Pulse width modulation, PWM, is used widely within the field of forinstance audio amplifiers. Generally, the available pulse widthmodulation techniques may be categorized into typically three differenttypes of pulse width modulation, natural pulse width modulation, NPWM,uniform pulse width modulation, UPWM or linearized pulse widthmodulation, hereinafter LPWM.

Generally, all pulse width modulation implies the technique oftransforming or converting an input signal into an output square wavesignal having a certain pulse width, at least partly defined by theinput signal by comparison of the input signal to a reference signal.

According to an embodiment of the invention, a simple iterative call ofthe established continuous signal representation, e.g. an interpolationpolynomial, will provide the desired intersection. It should be notedthat the established estimate may be provided without any complicatedroot solving and avoiding division and even square root.

According to the invention, the term intersection refers to a more orless accurate estimate of a true intersection between at least twocontinuous representations of two corresponding signals. Not only doessuch intersection typically refer to an estimate, but also the meaningof a true intersection should of course be understood in the light ofthe fact that a signal value between two discrete signal values is moreor less meaningless unless it refers to the originating analoguecontinuous time signal. In this light, the term intersection should ofcourse be understood quite broadly as the intersection between twosignals if they were both represented in the continuous time domain. Anintersection is also referred to within the art as a cross point.

It should be noted that a continuous signal representation, evidently,refer to a signal representation being continuous.

According to the invention a signal, e.g. the continuously representedsignal, may comprise a physical signal or a model of a physical signalor system.

According to an embodiment of the invention, said estimating ofintersections are performed in a pulse width modulation amplifier.

According to a most preferred embodiment of the invention, anintersection is provided for the purpose of obtaining the width of apulse width modulated signal of a pulse width modulator on the basis ofan input signal, which is compared to a reference signal.

According to an embodiment of the invention, whereby said intersectionsdetermine a pulse width modulated (PWM) output signal.

It should be noted that the shape of an output pulse width modulatedsignal according to the invention may vary according to the desiredapplication. Thus, although typical rectangular shaped pulses ispreferred to most application, derivations from the strict rectangularshape may occur, e.g. by the use of slightly curved output pulses. Suchoutput pulses may be somewhat difficult to handle but offer advantageousproperties with respect to harmonic distortion.

According to an embodiment of the invention, whereby said intersectionsdetermine the rising or a falling edge of a pulse width modulated (PWM)output signal.

According to an advantageous embodiment of the invention, the determinedintersection may advantageously be applied as determination of an edgeof a PWM, and may therefore result in a PWM signal having little or nodistortion. In this context it should again be remembered that thereduced distortion is obtained by relatively few computing operations.

According to an advantageous embodiment of the invention, the method ofdetermining the intersections may be applied in an audio PWM converter.

According to an embodiment of the invention, said discrete time domainsignal (DTB) comprises an input signal of a pulse width modulator andwhere

the other of said at least two continuous signal representations (SR1,SR2) comprising a reference signal on the basis of which a pulse widthmodulation of said input signal is established.

According to an embodiment of the invention, said reference signalcomprises a periodically function, preferably a sawtooth, a triangularor a curved waveform.

According to an embodiment of the invention, said reference signalcomprises a periodical signal and where the absolute value of thegradient is constant in each period.

According to an embodiment of the invention, said at least one iterativecall comprises at least one evaluation of the output of said continuousnon-linear signal representation when applying an input value. The inputvalue may be chosen in many different ways according to the invention.One preferred method, however, is to establish a start guess accordingto certain predefined criteria, apply this start guess as the inputvalue of the first iteration and then, subsequently, use the output ofthe resulting output of the non-linear continuous representation as theinput value of the next iteration. A start guess may of course be chosenaccording to many different more or less practical methods.

According to an embodiment of the invention, said at least one iterativecall comprises at least one evaluation of the output of an mirrorfunction of said continuous non-linear signal representation whenapplying an input value. Thus, the iteration may in this way convergetowards the only intersection between the function and the mirrorfunction.

According to an embodiment of the invention said at least one iterativecall comprises at least one evaluation of the output of a mirrorfunction of said continuous non-linear signal representation whenapplying an input value, said mirror function being established bymirroring of said continuous non-linear signal representation functionin a symmetry function.

According to an embodiment of the invention, said input value comprisesa start guess (SG).

According to a preferred embodiment of the invention, the input of aniteration may advantageously comprise an initial guess. This start guessmay preferably comprise a value close to the expected intersection.

The start guess may e.g. comprise the previous value or one of theprevious known values of the non-linear signal representation or aprevious value of the signal from which the non-linear signalrepresentation originates.

According to an embodiment of the invention, said input value comprisesthe output value of a previous iteration.

According to a preferred embodiment of the invention, the input of aniteration may preferably comprise the output of the previous iteration.In this way, an iteration converging towards the intersection may beestablished.

In an embodiment of the invention said at least two continuous signalrepresentations (SR1, SR2) comprises a non-linear representation of aninput signal and a periodic reference signal and where said referencesignal forms the symmetry function between said non-linearrepresentation of an input signal and said mirror function.

According to a preferred embodiment of the invention, the mirrorfunction of the non-linear representation of an input signal shouldpreferably be symmetrical during each period of and with respect to theperiodic reference signal, thus obtaining that a crossing between thenon-linear representation and the mirror function of the non-linearrepresentation represents exactly the intersection between thenon-linear representation and the symmetry function, i.e. the periodicreference signal.

One way of obtaining such a mirror function is quite straightforward andillustrated in the specification, i.e. applying a sawtooth signal asreference signal and where sawtooth signal has the gradient numericallyequals 1. In this way the mirror function may be established as theinverse function of the non-linear signal representation may easily befound by applying the output (=y−value) of a previous iteration step onthe non-linear signal representation and applying this as the input(=x−value) of the next iteration on the non-linear signalrepresentation. This switching between the non-linear signalrepresentation and the inverse function may be repeated as long as it isnecessary.

According to an embodiment of the invention, said symmetry function islinear. According to an embodiment of the invention, the symmetryfunction forming the symmetry line between the continuous representationand the applied mirror function may even comprise a curved symmetryline, although a mirror function which is actually the inverse functionof the curved continuos representation is preferred.

According to an embodiment of the invention, the gradient of the atleast one of said continuous signal representations (SR1, SR2) beingnon-linear is smaller than the other continuous signal representation.

According to a preferred embodiment of the invention, the gradient ofthe non-linear signal representation should be smaller than the gradientof the other signal. Thereby, it is ensured that the iteration mayactually provide a true estimate.

An example illustrating this fact is when an input signal, or rather themodel of this input signal is compared to a reference signal. If thegradient of the reference signal exceeds the gradient of the inputsignal, only one intersection is obtained in each period of thereference signal.

According to an embodiment of the invention, the gradient of the atleast one of said continuous signal representations (SR1, SR2) beingnon-linear is at least three times smaller, preferably five timessmaller than the other continuous signal representation.

When the other continuous signal representation is relatively quickvarying compared to the variation of the input signal representation, anintersection estimate may be established by using relatively fewiteration steps.

According to an embodiment of the invention, the signal bandwidth ofsaid non-linear signal representation being more than ten (10) timessmaller the signal bandwidth of the signal representation with which itis compared.

It should be noted that the iterative call(s) benefit(s) from the factthat the limitations on the bandwidth of the input signal and the curveform of the reference signal ensure that there is only one crossing perperiod if the reference signal, e.g. a rising sawtooth signal. Thesignal to which it is compared may in practical applications be thereference signal of a PWM modulator.

General, according to the terms applied according to the invention,bandwidth refer to the 3 dB bandwidth unless otherwise noted.

According to an embodiment of the invention, the signal bandwidth ofsaid non-linear signal representation being more than twenty (20) timessmaller the signal bandwidth of the signal representation with which itis compared.

According to an embodiment of the invention, the method may inparticular be applied within the audio field.

According to an embodiment of the invention, said iteration comprises arecursive call of said continuous signal representation or a derivativethereof.

When a function calls itself, it may simply be referred to as arecursion. A recursion may according to the context of the invention beregarded as a iterative call of the function, where the output of thefunction is fed back and utilized as an input (argument) to thefunction.

The recursive call, or the iteration, may be terminated when certainpredefined error margins are complied with. Other termination criteriamay simply be a termination upon the performing of a certain number ofiterations.

According to an embodiment of the invention, said iterative callinitiates an iteration sequence.

According to the invention an iteration sequence may be based on amathematical function, e.g. a model of a function based on a number ofdiscrete values. The mathematical function, i.e. the model, may beconstant during the complete iteration or it may vary over time, e.g.the number of iterations. In other words, some of the iterations may beperformed when using one mathematical model, and other iterations may beperformed when using another or other mathematical models.

According to an embodiment of the invention, said iteration sequencecomprises at least a first iteration group and where said firstiteration group is performed on a simplified mathematical model.

According to an embodiment of the invention, the first iterationsequence is performed on the basis of the established mathematical modelof the non-linear signal. However, the mathematical model has beensimplified when performing the first iteration(s) in order to obtain aninitial fast approach to the final result of the complete iterationsequence by means of reduced computational capacity, i.e. fewcalculations.

According to an embodiment of the invention, said iteration sequencefurther comprises at least one further iteration group and where saidfurther iteration is performed on a more complex mathematical model.

According to an advantageous embodiment of the invention, the lastiteration(s) should be performed with relatively high accuracy. In otherwords, if the first iterations have been performed on the basis of asimplified mathematical model of the non-linear signal, an increasing ofthe final resolution may be obtained by applying the more complex modelwhen closing in on the convergence point, i.e. the intersection.

According to a most preferred embodiment of the invention, an iterationsequence may simply comprise a first low-resolution iteration followedby a high-resolution iteration.

An example of such an iteration sequence may e.g. comprise a firstiteration, which is performed on the basis of a reduced 2^(nd) orderpolynomial and a second iteration, which is performed by a complete2^(nd) order polynomial.

According to an embodiment of the invention, at least one of saiditerative calls is established by means of a polynomial model comprising2^(nd) or higher order components, where at least one of thehigher-order components has been omitted.

According to a preferred embodiment of the invention, at least one orsome of the performed iterations are performed on reduced polynomialmodels. These iterations will advantageously comprise the initial orsome of the initial iterations of the complete iteration process.According to a very preferred embodiment of the invention, the completeiteration process comprises two iterations on a polynomial model, wherethe first iteration is performed by means of a reduced polynomial modeland the second is performed on a complete polynomial or at least a moredetailed polynomial. A reduced polynomial may for instance comprise a2^(nd) order polynomial of a signal, where the 2^(nd) order componenthas been omitted. Surprisingly, this “model-truncation” of the 2^(nd)order component reduces the final 3^(rd) order distortion combined withreduced computation.

Evidently, such model truncation may also be done when applying 3^(rd)or higher order polynomial, and where the higher-order or at least someof the even-order components are omitted in at least one of theiterations (preferably at least one of the first iterations).

According to an embodiment of the invention, said at least one iterativecall is established by applying a previous value of said continuoussignal representations representing a non-linear signal or a value ofthe non-linear signal as argument.

According to an embodiment of the invention, the at least one recursivecall is initiated by a start guess comprising one of the previous valuesof the discrete time domain signal or the (or one of the) continuousrepresentations thereof.

According to an embodiment of the invention, the argument of at leastone iterative call comprises the output of previous calls of thecontinuous signal representation of a non-linear signal.

According to an embodiment of the invention, said at least one iterationcomprises a predetermined fixed number of iterative recursive calls ofthe continuous representation.

According to an embodiment of the invention, the recursive calls may beterminated after a fixed number of recursive iterations. In this way,complicated stop-criteria may be avoided, and moreover, the calculatedintersection estimate may be obtained within a predictable time limit.

According to an embodiment of the invention, said fixed number ofiterations is less than 20 (twenty), preferably less than 10 (ten), evenmore preferably less than 5 (five).

According to an embodiment of the invention, it has been establishedthat even relatively few iterations may in fact result in a quitesatisfactory intersection estimate. Evidently, according to theinvention, the degree of satisfaction may highly depend on theapplication. In certain applications, a quick evaluation, e.g. performedin as little as two iterations may perfectly suffice, whereas otherapplications requiring higher precision may be performed when applyingfurther iterations.

According to an embodiment of the invention, whereby said at least oneof said continuous signal representations (SR1, SR2) being non-linear isrepresented by at least one mathematical model (MP).

According to the invention, a non-linear signal in general refers to asignal, which is anything but a pure linear function. In general, alinear function is a function defined by an equation of the formf(x)=y=mx+b. Thus, an example of a linear function is a 1^(st) orderpolynomial. An example of a non-linear function may e.g. be a 2^(nd) orhigher order polynomial. Another definition of a non-linearrepresentation in conformity with that of the invention is that the lineis curved.

According to an embodiment of the invention, said mathematical modelvaries over time.

According to an embodiment of the invention, a mathematical model may ona run-time basis be applied for approximation to a function or e.g. anumber of discrete points such as PCM samples. An example of suchapproximations may be a polynomial approximation to a number of signalsamples and where a new approximation is recalculated/remodeled incertain intervals. Such an interval may e.g. comprise a period of a PWMamplifier or converter.

In other words, a model varying over time may e.g. comprise a model,which is recalculated in each period of a PWM reference signal.

According to an embodiment of the invention, at least one of said signalrepresentations comprising a continuous representation of a discretetime domain signal (DTB).

According to a preferred embodiment of the invention, a model of adiscrete signal is established for the purpose of interpolating orextrapolating a part of the discrete signal, which is not available dueto the discrete nature of the signal.

Evidently, a continuous model may be established in different intervalsor in different proportion compared to the discrete signal. One modelmay e.g. cover the complete discrete signal, i.e. applied for thepurpose of recovering the complete “original” signal from which thediscrete values originates. Another model may e.g. only cover certainintervals or parts of the “original” signal, i.e. periods of the signalneeded for certain purposes. Such model may e.g. be chosen to cover onlyparts of a PWN input discrete signal, namely the parts of those wherethe input discrete signal intersect the reference signal.

According to an embodiment of the invention, said method comprising thestep of establishing a time varying continuous representation of adiscrete time domain signal (DTB) on a real-time basis.

According to an embodiment of the invention, the model is established ona real-time basis. An example of such real-time application may be in aconverter, e.g. a D/A-converter, where a real-time operation is needed.

According to an embodiment of the invention, said continuousrepresentation comprising a model of the signal curve fitted to thediscrete time domain signals (DTB).

According to an advantageous embodiment of the invention, the model isestablished in intervals for the purpose of obtaining a continuousrepresentation, which within a certain interval may be applied for thepurpose of determining a cross point, also referred to as anintersection, although fictive, between the discrete signal and anothersignal.

According to an embodiment of the invention, said continuousrepresentation comprising an interpolation polynomial.

According to a further embodiment of the invention, the continuousrepresentation may comprise an extrapolated model.

According to an embodiment of the invention, said continuousrepresentation comprising an interpolation of second or higher orderpolynomial of a non-linear signal.

According to a further embodiment of the invention, the polynomial maybe of other order than just two. Third or higher order polynomial may beapplied as well. In this context it should be noted that the inventionadvantageously facilitates the application of quite advanced signalmodels, which until now have been unrealistic. This is due to the factthat the computation needed for obtaining the desired intersection onthe basis of such models by finding of roots is more or less impossiblewith, at the time being available computation resources. According tothe invention, these values may simply be established by straightforwarditerations based in the model itself without any need for complicatedcomputation on the model.

According to an embodiment of the invention, said interpolationpolynomial comprises a second order polynomial function.

According to experiments, advantageous interpolations and intersectionshave been obtained by applying second order polynomials.

According to a preferred embodiment of the invention, the reference maybe regarded as a sought of symmetry function between the iteration modeland the inverse function of the iteration model. When keeping thereference signal linear, i.e. non-curved, throughout each period of thereference signal in a one-to-one relationship, the desired intersectionbetween the reference signal and the model of the signal may simply beobtained as a sequence of iterations based on the model f(x) and inversemodel h(x), the iterations resulting in a convergence towards theintersection point.

In an embodiment of the invention, said mirror function comprises theinverse function of said continuous non-linear signal.

According to a preferred embodiment of the invention, the inversefunction may simply be established as the inverse function of thenon-linear signal if the reference signal in each period forms asymmetry function where the slope numerically is one (1). Thisembodiment is quite advantageous due to the fact that the mirrorfunction then may be applied on the fly by simply shifting between X andY coordinates in the iteration.

Moreover, the invention relates to a pulse width modulator comprising

in input block for receipt of an input signal,

a reference signal generator provided for establishment of a referencesignal,

an intersection computing block

an output block establishing a pulse width modulated signal on the basisof a stream of intersections established by said intersection computingblock,

wherein estimation of a stream of intersections between the input signaland the reference signal is performed in said intersection computingblock by iterative calls of a function representing the input signal.

Moreover, the invention relates to a pulse width modulator comprising

in input block for receipt of an input signal,

a reference signal generator provided for establishment of a referencesignal,

an intersection computing block

an output block establishing a pulse width modulated signal on the basisof a stream of intersections established by said intersection computingblock,

wherein estimation of a stream of intersections between the input signaland the reference signal is performed in said intersection computingblock by iterative calls of a function representing the referencesignal.

Moreover, the invention relates to a pulse width modulator comprising

in input block for receipt of an input audio signal,

a reference signal generator provided for establishment of a referencesignal,

an intersection computing block

an output block establishing a pulse width modulated signal on the basisof a stream of intersections established by said intersection computingblock,

wherein estimation of a stream of intersections between the input signaland the reference signal is performed in said intersection computingblock according to any of the claims 1-34 and wherein one of thecontinuous signals represents an input signal of the pulse widthmodulator and wherein the other continuous signal represents a pulsewidth modulator reference signal.

In an embodiment of the invention at least one iterative call of afunction describing the input signal.

In an embodiment of the invention at least one iterative call at leastone iterative call of a function describing the reference signal.

The figures

The invention will now be described with reference to the drawings ofwhich

FIGS. 1 a-1 b illustrate the basic principle of PWM-modulation,

FIGS. 2 a-2 b illustrate the principles of dealing with discrete inputsignals,

FIG. 3 a to 5 b illustrate the iterations when applying the methodaccording to an embodiment of the invention in three differentrelationships between the input signal and the reference signal.

FIG. 6 a illustrates the convergence of the iterations to anintersection estimate,

FIGS. 6 b-6 c illustrate the convergence of the iterations to anintersection estimate,

FIGS. 7 a-7 b illustrate two different iteration processes within thescope of the invention

FIG. 8 illustrates a hardware implementation of one embodiment of theinvention and

FIG. 9 illustrates a block diagram of an embodiment of the invention.

DETAILED DESCRIPTION

FIG. 1 a and 1 b illustrate the basic properties and the nature of PWMmodulation.

It should be noted that the invention in general might be regarded asthe establishment of an intersection estimate between at least twocurves by means of computer calculations, where at least one of thecurves is a non-linear function. One of several applications is withinPWM (pulse width modulation) modulation, and the following explanationrefers to an application within this technical field.

The two signal representative curves SR1 and SR2 represent a PWMreference signal and a PWM input signal, respectively.

In the time continuous domain a PWM signal, i.e. the signal of FIG. 1 bis obtained by comparing the input signal representation with e.g. theoutput of a sawtooth generator. When the input signal is higher than thereference signal representation SR1, here a sawtooth, the PWM output ishigh and when the input signal is lower than the reference, the PWMoutput is low.

Such a switch point is illustrated in FIG. 1 a as CPE.

In the discrete time domain, we only have the “true” signal values witha given interval, i.e. a sample rate. This is illustrated in FIG. 2 a,where discrete points x(k−1), x(k) and x(k+1) represent an input signalSR2.

Evidently, discrete samples may not, or at least in very few cases,actually define the intersection between the input signal SR2 formed bya sequence of samples and the continuous reference signal representationSR1.

Therefore, a model MP of the input signal SR2 must be made in order toestablish an estimate of the cross points between input SR2 and thereference SR1. An example of such a model, which is a simple and costeffective model, may be a 2^(nd) order polynomial, which can be fittedto for instance three input samples, illustrated in FIG. 2 a by themathematical model MP. Evidently, in intervals, a new model should befound in order to ensure that a mathematical model is available at anyintersection between the input signal SR2 and the reference signal SR1.

In practice in a PWM application, one model MP should typically beestablished in each PWM period.

FIG. 2 b illustrates an example of several applicable ways ofestablishing a model on a run-time basis. According to the illustratedinterval on FIG. 2 b, three models Mn, Mn+1, Mn+2 have been established.Each of the illustrated models Mn, Mn+1, Mn+2 is established on thebasis of a three point 2^(nd) order polynomial approximation. In otherwords, the three models Mn, Mn+1, Mn+2 establish a combined curve. It isnoted that the applied models may be more or less advanced, and thecombined curve may be established in both a non-overlapping manner (asillustrated) and an overlapping manner. Higher order polynomials mayalso be applied.

According to this embodiment of the invention, a model is recalculatedin every second PWM period.

FIG. 2 c illustrates a further embodiment of the invention where themodels are established in an overlapping mode Mn, Mn+1, Mn+2. Whenapplying overlapping models, a clear strategy of how to obtain theintersection with the reference should be established. One applicablemethod may for instance be to establish the intersection between themodel Mn and the sawtooth signal Stn, i.e. between Mn+1 and the sawtoothsignal Stn+1, between Mn+2 and the sawtooth signal Stn+2, etc.

Note that the signal and axis are only illustrative to the basics ofPWM.

The illustrated model MP of FIG. 2 a can be found:${T \cdot p} = {\left. x\Leftrightarrow{{\begin{matrix}{t\left( {k - 1} \right)}^{0} & {t\left( {k - 1} \right)}^{1} & {t\left( {k - 1} \right)}^{2} \\{t(k)}^{0} & {t(k)}^{1} & {t(k)}^{2} \\{t\left( {k + 1} \right)}^{0} & {t\left( {k + 1} \right)}^{1} & {t\left( {k\quad + \quad 1} \right)}^{2}\end{matrix}} \cdot {\begin{matrix}p_{0} \\p_{1} \\p_{2}\end{matrix}}} \right. = {\begin{matrix}{x\left( {k - 1} \right)} \\{x(k)} \\{x\left( {k + 1} \right)}\end{matrix}}}$

If the time axis range in a single PWM period is chosen to go from −1.0to +1.0, we get −2, 0 and 2 for t(k−1), t(k) and t(k+1) respectively.With these t-values we get the following matrix equation:$\begin{matrix}{{{\begin{matrix}1 & {- 2} & 4 \\1 & 0 & 0 \\1 & 2 & 4\end{matrix}} \cdot {\begin{matrix}p_{0} \\p_{1} \\p_{2}\end{matrix}}} = \left. {\begin{matrix}{x\left( {k - 1} \right)} \\{x(k)} \\{x\left( {k + 1} \right)}\end{matrix}}\Leftrightarrow{\begin{matrix}p_{0} \\p_{1} \\p_{2}\end{matrix}} \right.} \\{= {{\begin{matrix}1 & {- 2} & 4 \\1 & 0 & 0 \\1 & 2 & 4\end{matrix}}^{- 1} \cdot {\begin{matrix}{x\left( {k - 1} \right)} \\{x(k)} \\{x\left( {k + 1} \right)}\end{matrix}}}} \\{= {{\begin{matrix}0 & 1 & 0 \\{- \frac{1}{4}} & 0 & \frac{1}{4} \\\frac{1}{8} & {- \frac{1}{4}} & \frac{1}{8}\end{matrix}} \cdot {\begin{matrix}{x\left( {k - 1} \right)} \\{x(k)} \\{x\left( {k + 1} \right)}\end{matrix}}}}\end{matrix}$

In other words, p₀ = x(k)$p_{1} = \frac{{x\left( {k + 1} \right)} - {x\left( {k - 1} \right)}}{4}$$p_{2} = \frac{{x\left( {k + 1} \right)} - {2 \cdot {x(k)}} + {x\left( {k - 1} \right)}}{8}$

So the coefficients for the second order polynomial describing thecontinuous domain signal can be found using shift and add operations.

In order to establish the desired intersection a conventional way offinding the roots in the polynomial would of course be to use theanalytical solution:$x_{cross} = {\frac{{- b} \pm \sqrt{b^{2} - {4 \cdot a \cdot c}}}{2 \cdot a} = \frac{{- \left( {p_{1} - 1} \right)} \pm \sqrt{\left( {p_{1} - 1} \right)^{2} - {4 \cdot p_{0} \cdot p_{2}}}}{2 \cdot p_{0}}}$

But the square root and division do not seem like attractive solutions.Consequently, prior art solutions focus on somewhat less complicatedalgorithms, involving reduced complexity mathematical models.

According to the invention, another approach to the intersectionestimation is applied.

Supposing that the input signal SR2 is highly over sampled and bandlimited, which ensures that the slew rate (gradient) of the signalalways is lower than the reference. And there is only one single crosspoint in one PWM period.

A nice feature of many mathematically functions, including a polynomialof second order, is that, when called recursively, they approach thepoint of the function, where the function input equals the functionoutput if the first derivative of the function at this point is lessthan one. And this point equals the point where the function crosses thesawtooth SR1, f(x)=x, i.e. the sought intersection.

FIGS. 3 a, 3 b, FIGS. 4 a, 4 b and FIGS. 5 a and 5 b illustrate threeexamples of iterative findings of intersection estimates according toembodiments of the invention. The estimate of the intersection is foundusing the scheme listed below, i.e. an iterative call of themathematical model. x = start guess; for(k=0; k<N_ITER; k++) {  x =f(x); }

The mathematically function in these examples are a sinusoidal.

In FIGS. 3 a and 3 b, illustrating an iterative estimation according toan embodiment of the invention, the signal bandwidth of reference signalSR1 is five times the bandwidth of input signal SR2.

The y-axis of FIG. 3 a represents the function value of the referenceand input signal representations and FIG. 3 b illustrates the absoluteerror in dB of the estimated intersection as a function of the number ofiterations.

When investigating the obtained result it is noted that the iterativemethod according to the invention may even be applied when the referencesignal is relatively comparable to the input signal, of course dependingon the application in which the method is applied.

According to the illustrated embodiment of the invention, each iterationimproves the intersection estimate with approximately 6 dB.

Note that the improvements obtained during each iteration aresubstantially independent of the quality of the start guess, i.e. theinitial iteration value upon which the iteration is based.

In FIGS. 4 a and 4 b, illustrating a further iterative estimationaccording to an embodiment of the invention, the signal bandwidth ofreference signal SR1 is ten times the bandwidth of input signal SR2.

The y-axis of FIG. 4 a represents the function value of the referenceand input signal representations and FIG. 4 b illustrates the absoluteerror in dB of the estimated intersection as a function of the number ofiterations.

According to the illustrated embodiment of the invention, each iterationimproves the intersection estimate with approximately 12 dB.

In FIGS. 5 a and 5 b, illustrating a first iterative estimationaccording to an embodiment of the invention, the signal bandwidth ofreference signal SR1 is twenty times the bandwidth of input signal SR2.This corresponds approximately to a 20 kHz input signal full scale and aPWM rate, i.e. SR1, on 400 kHz.

The y-axis of FIG. 5 a represents the function value of the referenceand input signal representations and FIG. 5 b illustrates the absoluteerror in dB of the estimated intersection as a function of the number ofiterations.

According to the illustrated embodiment of the invention, each iterationimproves the intersection estimate with approximately 18 dB.

In the above, the X-axis represents a normalized time axis and they-axis represents a normalized Y-axis

FIGS. 3 a, 4 a and 5 a s illustrate the consecutive samples whereasFIGS. 3 b, 4 a and 5 b illustrate the resulting error on theintersection estimate during the performed iterations.

As seen on the two figures above, the most accurate results, using agiven number of iterations, are obtained when the slew rate (i.e. thegradient) of the input signal is low compared to the slew rate of thereference signal.

FIG. 6 a illustrates a way of validating the method according to whichit must be ensured that the cross point estimate,—also referred to asintersection, gets closer to the true cross point (xt) after each singleiteration.

In other words, the function output value must be closer to the truecross point than the function input value. This is the case whenymin<f(xe)<ymax.

ymin=xe=lower convergence limit

ymax=2·xt−xe=upper convergence limit xt = f(xe) + ∫_(xe)^(xt)f^(′)(x)𝕕xwhere${f^{\prime}(x)} = {\left. \frac{\mathbb{d}{f(x)}}{\mathbb{d}x}\Updownarrow{f({xe})} \right. = {{xt} - {\int_{xe}^{xt}{{f^{\prime}(x)}{\mathbb{d}x}}}}}$

and since −1<f′(x)<1 we get:

xe=ymin<f(xe)<ymax=2·xt−xe, thereby validating that an intersection mayactually be found.

As mentioned above, the intersection point will typically not be locatedas a cross-point between the “true” continuous input signal and thereference, e.g. a sawtooth reference, but it will be estimated as thecrossing between a mathematical model, e.g. a polynomial model, and thereference.

So we face two different kinds of errors in the intersection estimation:

-   -   The polynomial model (second order) is not perfect    -   We have to choose a finite number of iterations to locate the        intersection

Experiments has, however, shown that the desired performance can bereached using only two iterations, when the PWM frequency isapproximately 20 times the signal bandwidth in a PWM amplifierapplication. Evidently, such a result is impressing in particular whenapplied in the context of mathematical models of non-linear functions,which until now have been extremely complex to deal with.

Evidently, other numbers of iterations than two may be applied for otherpurposes and other iteration termination criteria may be appliedaccording to the invention.

FIGS. 6 b and 6 c illustrates a more conceptual understanding of anembodiment of the invention. The X-axis represents a normalized timeaxis and the y-axis represents a normalized Y axis.

In FIG. 6 b the function f(x) represents a given model of an inputsignal. The function has an inverse representation, h(x) (here=f⁻¹(x))in the sense that it is symmetrical with respect to a symmetry functiong(x). There is only one intersection between the function and theinverse function. This point is the intersection point. Typically andpreferably, the symmetry axis formed by the symmetry function g(x) is inpractice formed by e.g. a reference sawtooth having a slope which equalsone. Other examples may e.g. be triangular waveform This means inpractice that a first start guess SG will result in a first output valueof f(x), OV1. This value will, when applied as an argument to the modelf(x) in fact correspond to providing the inverse function f⁻¹(x), whichagain provides an output value OV2 and so forth up to OV5 will in thiscase correspond to the desired intersection estimate. It is clear fromthe illustration that further iterations will improve the quality of theintersection estimate itself. In practice, when applying a 2^(nd) orpolynomial order model f(x) of an input signal, only two iterations willprovide a quite impressing intersection estimate, here: OV2.

Note that the inverse function is simply obtained by applying the outputof each iteration step as the input to the next iteration on the samefunction, here f(x). In other words, in this illustrated embodimentthere will be no need to establish an inverse function of f(x).

In FIG. 6 c a further feature of the invention is illustrated. In thisembodiment the curved representation f(x) is compared with a curvedrepresentation g(x). In this quite advanced embodiment, the intersectionestimate may be established by establishing an mirror function h(x) off(x) on the basis of g(x), i.e. where g(x) forms the symmetry functionbetween h(x) and f(x). In this case, a curved reference signal may infact be applied and an intersection estimate may still be obtained byfew iterations by switching between the model f(x) and the inverseversion of it, namely h(x).

An alternative approach than the illustrated of FIGS. 6 b and 6 c is,when facing a curved symmetry function g(x), to transform f(x) into afunction f′(x) through g⁻¹(x). Perform the desired iterations in the“linear domain” corresponding to the illustrated iteration of FIG. 6 band the transform the obtained intersection back into the originaldomain, here corresponding to FIG. 6 c. In this way, complex computationfor the purpose of finding the mirror function may be avoided.

FIG. 7 a and FIG. 7 b illustrate two examples of many applicableiteration processes within the scope of the invention.

In both embodiments, the reference function is a sawtooth signal, wheref(x)=x in each period.

The iteration process illustrated in FIG. 6 a comprises two iterations:y ₀ =x(k)=start guessy ₁ =p ₀ +p ₁ ·y ₀ +p ₂ ·y ₀ y ₀y ₂ =p ₀ +p ₁ ·y ₁ +p ₂ ·y ₁ ·y ₁

That sums up to six multiplications and four additions.

A simplified iteration process as illustrated in FIG. 7 b also comprisestwo iterations. However, in order to reduce the computer power (silicon)needs, the first of the two iterations can be simplified simply bythrowing the “square part” away:y ₀ =x(k)=start guessy ₁ =p ₀ +p ₁ ·y ₀y ₂ =p ₀ +p ₁ ·y ₁ +p ₂ y ₁ ·y ₁

Now we only need 4 multiplications and 3 additions.

A very interesting observation is that the 3^(rd) harmonic, which is themost annoying error component in audio applications, of the sparsesolver output has a lower level than the true solver output. Again, itshould be noted that this suppression of undesired 3^(rd) order harmonicdistortion is obtained while at the same time reducing the computations.

Turning now to a hardware application, the polynomial coefficients maybe calculated as:p ₀ =x(k)p ₁=(x(k+1)−x(k−1))·0.25p ₂=(x(k−1)−2·x(k)+x(k+1))·0.125

Since the input signal has a low bandwidth, e.g. approximately 20 kHzcompared to the applied sample rate, e.g. 384 kHz, the p₁ and p₂ valueswill have low amplitude.

So to optimize the dynamic range of these values, the coefficients arescaled up and corrected later in the two iterations, like below:p ₀ =x(k)p ₁ =x(k+1)−x(k−1)p ₀ =x(k+1)−2·x(k)+x(k−1)y ₀ =x(k)=p ₀=start guessy₁=p₀+p₁·y₀·0.25y₂=p₀+p₁·y₁0.25+p₂·y₁·y₁·0.125

FIG. 8 illustrates an example of an implementation diagram of the abovelisted algorithm. The illustrated hardware structure at a given timeinitially establishes the model coefficients, p₀, p₁ and p₂, readingfrom left to right. Thereafter two iterations are performed and Outrepresents the final output value.

Numerous other structures or hardware may be applied within the scope ofthe invention.

The illustrated algorithm may e.g. be implemented in a conventional DSP,FPGA, ASIC, PLD, CPLD or any other suitable signal processing structure.

In the following example the performance of the method according to anembodiment of the invention, when the input signal is 6.66 KHz, 90% fullscale and where the PWM, e.g. SR1 is over sampled by eight times, i.e.384 KHz.

According to the below examples, the sawtooth is single-sided and thePWM signal is a two-level signal. The fourth example, algorithm A,represents the above described embodiment of the invention compared tothe algorithms A to C representing algorithms well known within the art.THD 2^(nd) 3^(rd) Mult Add Shft Comp Abs A −88 dB −90 dB −117 dB 7 9 0 00 B −113 dB  −115 dB  −133 dB 14 11 0 1 0 C −84 dB −92 dB  −87 dB 6 6 00 1 D −85 dB −87 dB −124 dB 4 6 4 0 0

THD refers to the total harmonic distortion. In this case, with an inputsignal of 6.66 kHz, the total error comprises the 2^(nd) and 3^(rd)order errors, represented in the second and third column.

However, when comparing the efficiency of the above-applied methods itis noted that the method applied according to an embodiment of theinvention features a relatively impressing performance on the basis ofvery few calculations. In particular it is noted that the harmonicdistortion originating from the 3^(rd) order harmonic is −124 dBcompared to the result obtained according to algorithm B of −133 dB,where the result according to the invention is obtained by, compared toalgorithm B, very few calculations.

This is quite significant when applying the invention in audioapplications due to the fact that 3^(rd) order harmonics represent themost undesired distortion. This is due to the fact that odd-orderharmonic distortion has been recognized far more annoying to the humanear than even-order harmonics.

In other words, according to the invention, an advantageous method ofestablishing an intersection between two signal representations, whereat least one of the representations may be curved, due to the fact thatthe method may be performed with very little computing and, e.g. inaudio applications, with very impressing results.

In this context is should be noted that the algorithm according to theinvention may be performed in a hardware implementation in e.g. FPGA,ASIC, PLD, CPLD, where relevant mathematical operations other thanmultiplication and addition may be performed “free of charge”.

Finally, it should be emphasized that the invention is in particularadvantageous when applied in e.g. FPGA, ASIC, PLD, CPLD due to the factthat additions may be performed with relatively little computationaleffort in the computer.

One of several applications in which the above-described method may e.g.be applied according to a preferred embodiment of the invention is in aPWM amplifier comprising digital input, e.g. for high resolution audio,e.g. 24 bit, at a sample rate of e.g. 44.1 kHz or 48 kHz.

The digital input is then delivered to an upsampling asynchronous orsynchronous sample rate converter, upsampling the input signal to thesame rate as the PWM switch frequency, e.g. 384 kHz (=8×48 kHz).

The upsampled signal may then be compared to a reference signalaccording to the above described methods and the edges of a PWM signalmay be determined. The established edges may then quantized and noiseshaped to pulse widths having a somewhat lover resolution. The noiseshaping ensures that the quantization error is suppressed within theaudio band.

Subsequently, a pulse generator establishes the calculated switch timesto a physical signal, e.g. via a power stage such as a FET push-pullstage, i.e. a current amplifier.

Finally, the application may involve a demodulation filter and aloudspeaker.

FIG. 9 illustrates an example of an application of the presentinvention. The illustrated system comprises a PWM amplifier/audiosystem.

The system comprises an input block 1901 adapted for receipt of a codedaudio signal. The input block 1901 branches the input signal into twoprinciple different directions; in one direction for the purpose ofconverting the information coded in the input signal into a relevant PWMrepresentation and one direction for the purpose of establishing a clockreference signal on the basis of the input signal.

The latter direction is represented by a PLL clock-synchronizing block1902 referring to a high-frequency oscillator block 1903.

The first principle direction starts with the upsampling block 1904basically transforming the input signal from one sampling frequencyrepresentation into an N times higher sampling representation.

The upsampled signal is then fed to an intersection-computing block 1905adapted for determination of intersections with a parallel referencesignal representation according to an embodiment of the invention. Theintersections may e.g. be established in the block 1905 according to theprinciples of FIGS. 7A and 7B. The consecutive noise shaping andquantizing block 1906 feeds the established intersections a PWM pulsegenerator, in this case a true differential three level generator 1908referring to the high frequency generator 1903.

The resulting PWM signal is then fed to a power stage 1909 and fromthere via a demodulator 1910 to a loudspeaker 1911.

Evidently, the above-mentioned application only describes one of severalapplications within the scope of the invention.

An example of an application in which the present invention may beapplied is disclosed in PCT DK03/00475, hereby incorporated byreference.

A further example in which the invention may advantageously be appliedis EP 1178388 A1, hereby incorporated by reference.

1. Method of estimating an intersection between at least two continuoussignal representations (SR1, SR2) in a pulse width modulator, at leastone of said continuous signal representations (SR1, SR2) beingnon-linear, said method comprising the step of providing an intersectionestimate (CPE) between said at least two continuous signalrepresentations on the basis of at least one iteration comprising atleast one iterative call of a function describing said continuous signalrepresentations (SR1, SR2) being non-linear and whereby said estimatingof intersections are performed in a pulse width modulation modulator. 2.Method of estimating an intersection between at least two continuoussignal representations according to claims 1, whereby a stream of saidintersection estimates determine a pulse width modulated (PWM) outputsignal of the pulse width modulator.
 3. Method of estimating anintersection between at least two continuous signal representationsaccording to claim 1, whereby said intersections determine a rising or afalling edge of a pulse width modulated (PWM) output signal of the pulsewidth modulator.
 4. Method of estimating an intersection between atleast two continuous signal representations according to any of theclaims 1, at least one of said signal representations comprising acontinuous representation of a discrete time domain signal (DTB). 5.Method of estimating an intersection between at least two continuoussignal representations according to claim 4, whereby said discrete timedomain signal (DTB) comprises an input signal of a pulse width modulatorand where the other of said at least two continuous signalrepresentations (SR1, SR2) comprising a reference signal on the basis ofwhich a pulse width modulation of said input signal is established. 6.Method of estimating an intersection between at least two continuoussignal representations according to claim 5, said reference signalcomprising a periodically function, preferably a sawtooth, a triangularor a curved waveform.
 7. Method of estimating an intersection between atleast two continuous signal representations according to claim 5,whereby said reference signal comprises a periodical signal and where anabsolute value of a gradient is constant in each period.
 8. Method ofestimating an intersection between at least two continuous signalrepresentations according to claim 1, whereby a mirror functioncomprises an inverse function of said continuous non-linear signal. 9.Method of estimating an intersection between at least two continuoussignal representations according to claim 1, whereby said at least oneiterative call comprises at least one evaluation of output of saidcontinuous non-linear signal representation when applying an input value(IV).
 10. Method of estimating an intersection between at least twocontinuous signal representations according to claim 1, whereby said atleast one iterative call comprises at least one evaluation of the outputof a mirror function of said continuous non-linear signal representationwhen applying an input value (IV), said mirror function beingestablished by mirroring of said continuous non-linear signalrepresentation function in a symmetry function.
 11. Method of estimatingan intersection between at least two continuous signal representationsaccording to claim 10, where said input value comprises a start guess(SG).
 12. Method of estimating an intersection between at least twocontinuous signal representations according to claim 10, where saidinput value comprises an output value of a previous iteration. 13.Method of estimating an intersection between at least two continuoussignal representations according to claim 10, whereby said at least twocontinuous signal representations (SR1, SR2) comprises a non-linearrepresentation of an input signal and a periodic reference signal andwhere said reference signal forms the symmetry function between saidnon-linear representation of an input signal and said mirror function.14. Method of estimating an intersection between at least two continuoussignal representations according to claim 13, whereby said symmetryfunction is linear.
 15. Method of estimating an intersection between atleast two continuous signal representations according to claim 1,whereby a gradient of the at least one of said continuous signalrepresentations (SR1, SR2) being non-linear is smaller than the othercontinuous signal representation.
 16. Method of estimating anintersection between at least two continuous signal representationsaccording to claim 1, whereby a gradient of the at least one of saidcontinuous signal representations (SR1, SR2) being non-linear is atleast three times smaller, preferably five times smaller than the othercontinuous signal representation.
 17. Method of estimating anintersection between at least two continuous signal representationsaccording to claim 1, a signal bandwidth of said non-linear signalrepresentation being more than ten (10) times smaller a signal bandwidthof the signal representation with which it is compared.
 18. Method ofestimating an intersection between at least two continuous signalrepresentations according to claim 1, a signal bandwidth of saidnon-linear signal representation being more than twenty (20) timessmaller a signal bandwidth of the signal representation with which it iscompared.
 19. Method of estimating an intersection between at least twocontinuous signal representations according to claim 1, whereby saiditeration comprises a recursive call of said continuous signalrepresentation or a derivative thereof.
 20. Method of estimating anintersection between at least two continuous signal representationsaccording to claim 19, whereby said iterative call initiates aniteration sequence.
 21. Method of estimating an intersection between atleast two continuous signal representations according to claim 20,whereby said iteration sequence comprises at least a first iterationgroup and where said first iteration group is performed on a simplifiedmathematical model.
 22. Method of estimating an intersection between atleast two continuous signal representations according to claim 21,whereby said iteration sequence further comprises at least one furtheriteration group and where said further iteration is performed on a morecomplex mathematical model.
 23. Method of estimating an intersectionbetween at least two continuous signal representations according toclaim 1, whereby at least one of said iterative calls is established bymeans of a polynomial model comprising 2^(nd) or higher orderscomponents, where at least one of the high-order component has beenomitted.
 24. Method of estimating an intersection between at least twocontinuous signal representations according to claim 1, whereby said atleast one iterative call is established by applying a previous value ofsaid continuous signal representations representing a non-linear signalor a value of the non-linear signal as argument.
 25. Method ofestimating an intersection between at least two continuous signalrepresentations according to claim 25, whereby the argument of at leastone iterative calls comprises an output of previous calls of thecontinuous signal representation of a non-linear signal.
 26. Method ofestimating an intersection between at least two continuous signalrepresentations according to claim 1, whereby said at least oneiteration comprises a predetermined fixed number of iterative recursivecalls of the continuous representation.
 27. Method of estimating anintersection between at least two continuous signal representationsaccording to claim 26, whereby said fixed number of iterations is lessthan 20 (twenty), preferably less than 10 (ten), even more preferablyless than 5 (five).
 28. Method of estimating an intersection between atleast two continuous signal representations according to claim 1,whereby said at least one of said continuous signal representations(SR1, SR2) being non-linear is represented by at least one mathematicalmodel (MP).
 29. Method of estimating an intersection between at leasttwo continuous signal representations according to claim 28, wherebysaid mathematical model varies over time.
 30. Method of estimating anintersection between at least two continuous signal representationsaccording to claim 1, said method comprising the step of establishing atime varying continuous representation of a discrete time domain signal(DTB) on a real-time basis.
 31. Method of estimating an intersectionbetween at least two continuous signal representations according toclaim 30, said continuous representation comprising a model of thesignal curve fitted to the discrete time domain signals (DTB). 32.Method of estimating an intersection between at least two continuoussignal representations according to claim 30, said continuousrepresentation comprising an interpolation polynomial.
 33. Method ofestimating an intersection between at least two continuous signalrepresentations according to claim 30, said continuous representationcomprising an interpolation of second or higher order polynomial of anon-linear signal.
 34. Method of estimating an intersection between atleast two continuous signal representations according to claim 32,whereby said interpolation polynomial comprises a second orderpolynomial function.
 35. Hardware structure comprising means forperforming the method according to claim
 1. 36. Hardware structureaccording to claim 35, wherein said hardware structure comprises DSP,FPGA, ASIC, PLD, CPLD or any other suitable signal processing structure.37. Programming code for establishing the method according to claim 1 ina hardware structure.
 38. Data carrier comprising the programming codeof claim 37
 39. Pulse width modulator comprising in input block forreceipt of an input signal, a reference signal generator provided forestablishment of a reference signal, an intersection computing block anoutput block establishing a pulse width modulated signal on the basis ofa stream of intersections established by said intersection computingblock, wherein estimation of a stream of intersections between the inputsignal and the reference signal is performed in said intersectioncomputing block by iterative calls of a function representing the inputsignal.
 40. Pulse width modulator comprising in input block for receiptof an input signal, a reference signal generator provided forestablishment of a reference signal, an intersection computing block anoutput block establishing a pulse width modulated signal on the basis ofa stream of intersections established by said intersection computingblock, wherein estimation of a stream of intersections between the inputsignal and the reference signal is performed in said intersectioncomputing block by iterative calls of a function representing thereference signal.
 41. Pulse width modulator comprising in input blockfor receipt of an input audio signal, a reference signal generatorprovided for establishment of a reference signal, an intersectioncomputing block an output block establishing a pulse width modulatedsignal on the basis of a stream of intersections established by saidintersection computing block, wherein estimation of a stream ofintersections between the input signal and the reference signal isperformed in said intersection computing block according to claim 1 andwherein one of the continuous signals represents an input signal of thepulse width modulator and wherein the other continuous signal representsa pulse width modulator reference signal.
 42. Pulse width modulatoraccording to claim 41, wherein said at least one iterative call is acall of a function describing the input signal.
 43. Pulse widthmodulator according to claim 41, wherein said at least one iterativecall is a call of a function describing the reference signal.